CN106501357B - A method of measurement mixed gas molecule multi-mode relaxation process - Google Patents
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Abstract
The invention discloses a kind of methods for measuring mixed gas molecule multi-mode relaxation process, its sound spectrum expression formula by establishing single relaxation, in ω τ=1, obtain the generic representation form of the single relaxation process of sound spectrum, and then the expression-form of multi-mode relaxation process effective heat capacity is obtained, by the acoustical absorptivity α for measuring 2*N Frequency pointr(ω) and velocity of sound c (ω) obtains 2*N dimensionless sound relaxation absorption coefficient μm(ω) solves N number of ε from 2*N equationiAnd τiValue, and by N number of εiAnd τiValue substitute into original equation in, so that it may obtain μmThe spectral line of (ω) about the π of ω=2 f, can rebuild multi-mode relaxation process.The method that the present invention measures mixed gas molecule multi-mode relaxation process is not only easy to operate, and it can accurately reconstruct the complete spectral line of multi-mode relaxation process, for the gas sensor accurate measuring technique decomposed based on sound spectrum, a kind of more adaptable, sound spectrum measurement method that can be practical is provided.
Description
Technical field
The invention belongs to gas sensor technical field, it is related to what a kind of mixed gas molecule multi-mode relaxation process was rebuild
Method.
Technical background
The sensing technology for being able to detect gas componant at present mainly has: chemical reaction, semiconductor, gas-chromatography and infrared light
The technologies such as absorption, heat transfer are composed, but there is respective advantage and disadvantage for these technologies.Mixed gas molecule multi-mode based on sound spectrum
The gas sensor technology of relaxation process measurement, principle are that have using the sound absorption of different frequency and velocity of sound frequency dispersion spectral line with gas
The characteristic that body ingredient changes and changes is capable of detecting when so as to directly obtain the outstanding advantage of gas molecule structural information
The different kinds and concentrations of mixed gas are one of most potential gas sensing techniques emerging at present.In environmental monitoring, gas
The fields such as body discharge, industrial stokehold are with a wide range of applications.Its measurement method is simple, measurement accuracy is high, the service life is long,
Can non-destructive testing and real-time online detection, eliminate other gas sensors and need the trouble calibrated.
In the measurement method of traditional sound spectrum, operator needs the pressure of constantly variation gas cavity, needs to measure gas close
The cumbersome operating process such as degree and pressure, and can only obtain coarse single relaxation process spectral line.In order to overcome traditional sound spectrum
The case where constantly changing gas pressure intensity is needed in measurement method, paper " Synthesizing Primary Molecular
Relaxation Processes in Excitable Gases Using a Two-Frequency Reconstructive
Algorithm”(A. G.Petculescu,R.M.Lueptow.Physical Review Letters,2005,94(23):
238301) it proposes a kind of without changing chamber pressure, the sounding magnitude synthetic gas molecular relaxation mistake based on two Frequency points
The algorithm for reconstructing of journey thermal capacitance.This algorithm is that the relationship between effective heat capacity and frequency using gas is rebuild, and needs to survey
The density and pressure of gas are measured, measurement method is cumbersome and complicated.
To solve the above-mentioned problems, paper " Algorithm for capturing primary relaxation
processes in excitable gases by two-frequency acoustic measurements”
(K.S.Zhang,S.Wang,M.Zhu,Y.Ding.Measurement Science and Technology,2013,24(5):
055002.) it using the relationship between sound relaxation spectrum and frequency, improves Petculescu and Lueptow (referred to as PL) and proposes
Algorithm, have no need to change the pressure of gas cavity, do not need measurement gas density and pressure, simplify measurement method and measurement
Operation.But this method for fast measuring is adapted to the main internal relaxation process situation of only one in mixed gas, it is uncomfortable
With the mixed gas for having multiple main relaxation processes, it will lead to some important relaxation information and lose.
Summary of the invention
Aiming at the above defects or improvement requirements of the prior art, the present invention provides a kind of mixed gas molecule multi-mode relaxations
The method that Henan process is rebuild, sound absorption and acoustic velocity value of this method by 2*N Frequency point of measurement, obtains N number of list by algorithm
The relaxation time of relaxation process and relaxation strength eliminate measurement density to accurately rebuild entire multi-mode relaxation process
With the troublesome operation of pressure.
Above-mentioned purpose to realize the present invention, the present invention provide what a kind of mixed gas molecule multi-mode relaxation process was rebuild
Method, this method comprises the following steps:
(1) the sound spectrum expression formula of single relaxation is determined are as follows:
Wherein,Indicate the sum of translation and rotation thermal capacitance,Indicating the vibration thermal capacitance of molecule, the π of ω=2 f is angular frequency,
F is frequency, and τ is the relaxation time,
(2) according to the sound spectrum expression formula of single relaxation, in ω τ=1, the general purpose table of the single relaxation process of sound spectrum is obtained
Show form:
Wherein, μi(ω) indicates that dimensionless relaxation absorption coefficient, R are gas universal constant；
(3) assume in mixed gas to include W kind molecular species, there is N kind vibration mode, effective heat of multi-mode relaxation process
Appearance is the sum of single relaxation process of intramolecule:
Wherein, τiIt is defined as the Henan time of the single relaxation process in inside in entire multi-mode relaxation process；
(4) peak value is definedFor relaxation time τiCorresponding relaxation strength, obtains:
Wherein,αr(ω) is acoustical absorptivity, and λ is wave length of sound, and c (ω) is sound
Speed value；
(5) the acoustical absorptivity α of 2*N Frequency point is measuredr(ω) and velocity of sound c (ω), obtains 2*N μm(ω), from 2*N
N number of ε is solved in a equationiAnd τiValue, and by N number of εiAnd τiValue substitute into step (4), obtain μm(ω) is about the π of ω=2 f's
Spectral line can rebuild multi-mode relaxation process.
Further, the vibration thermal capacitance of the moleculeAre as follows:
Wherein, g is the degeneracy of vibration mode, θintFor characteristic vibrational temperature, T0For temperature.
Further, the characteristic vibrational temperature θintAre as follows:
Wherein: h is planck constant, kBFor Boltzmann constant, υ is vibration frequency.
Further, the preparation method of the sound spectrum expression formula of the single relaxation are as follows:
(11) sound wave is propagated in gas, effective angular wave numberIt can be written as velocity of sound c (ω) and molecular relaxation absorbs system
Number αrThe form of (ω) expression:
(12) indicate that effective angular wave number can be used in dimensionless relaxation absorption coefficient, μ (ω) with μ (ω)Real and imaginary parts table
Show:
Wherein,For effective angular wave numberImaginary part,For effective angular wave numberReal part；
(13)With effective heat capacityThere are following relationships:
Wherein, ρ0And p0The density and pressure of gas when respectively balancing；
(14) it enablesObtain the sound spectrum representation of gas multi-mode relaxation process:
μ (ω)=AμY (ω),
(15) sound spectrum of a multi-mode relaxation process can be resolved into the sound spectrum expression formula of multiple single relaxation processes.
Further, the negative of the real and imaginary parts of the multi-mode relaxation process are as follows:
In general, through the invention it is contemplated above technical scheme is compared with the prior art, have below beneficial to effect
Fruit:
(1) method of the invention, sound absorption and acoustic velocity value by 2*N Frequency point of measurement, obtains N number of list by algorithm
The relaxation time of relaxation process and relaxation strength eliminate measurement density to accurately rebuild entire multi-mode relaxation process
With the troublesome operation of pressure；
(2) method of the invention, improve causes some important relaxation information to be lost in some cases in Zhang Kesheng algorithm
The weakness of mistake has rebuild the molecular relaxation spectrum of mixed gas, more accurately for the essence of the gas sensing techniques based on sound relaxation spectrum
Really measurement proposes a kind of more adaptable, measurement method that can be practical.
Detailed description of the invention
Fig. 1 (a) is the reconstruct schematic diagram of the gas molecule relaxation process in the embodiment of the present invention, mixed gas 40%
CH4-10%Cl2-50%N2；
Fig. 1 (b) is the reconstruct schematic diagram of the gas molecule relaxation process in the embodiment of the present invention, mixed gas 5%
CH4- 95%N2；
Fig. 2 (a) is the reconstruct schematic diagram of the gas molecule relaxation process in another embodiment of the present invention, and mixed gas is
10%CO2-90%O2, T=600K；
Fig. 2 (b) is the reconstruct schematic diagram of the gas molecule relaxation process in another embodiment of the present invention, and mixed gas is
10%CO2-90%O2, T=450K.
Specific embodiment
In order to more clearly from explain technical solution of the present invention, with reference to the accompanying drawings and detailed description to the present invention
It is described in further detail, following embodiment is only for explaining the present invention, and does not constitute a limitation of the invention.Under in addition,
Technical characteristic involved by each embodiment of the present invention described in face is as long as they do not conflict with each other
It is combined with each other.
The method that a kind of mixed gas molecule multi-mode relaxation process of the embodiment of the present invention is rebuild, detailed process is such as
Under:
When sound wave is propagated in gas, effective angular wave numberIt can be written as velocity of sound c (ω) and molecular relaxation absorbs system
Number αrThe form of (ω) expression:
Wherein the π of ω=2 f is angular frequency, and f is frequency,
Dimensionless relaxation absorption coefficient is indicated with μ (ω)r(ω) λ, wherein λ is wave length of sound, wavelength be equal to the velocity of sound divided by
Frequency.Effective angular wave number can be used in μ (ω)Real and imaginary parts indicate:
Wherein,For effective angular wave numberImaginary part,For effective angular wave numberReal part.
In thermodynamics,With effective heat capacityThere are following relationships:
Wherein ρ0And p0The density and pressure of gas, R=8.31Jmol when respectively indicating balance-1·K-1It is that gas is pervasive
Constant.
From formula (2) and formula (3) as can be seen that effective heat capacityDetermine the sound spectrum and relaxation process of gas.
Formula (1) and formula (3) are squared, simultaneous formula (2), are enabledIt is available:
X (ω) and y (ω) is effective heat capacity respectivelyReal and imaginary parts negative.
Formula (4) is the sound spectrum representation of the single relaxation process of gas and multi-mode relaxation process, using this formula,
The sound spectrum of one multi-mode relaxation process can be resolved into the sound spectrum of multiple single relaxation processes.
Sound spectrum expression formula under single relaxation are as follows:
Wherein τ indicates the relaxation time,Indicate external thermal capacitance, that is, the translation thermal capacitance and the sum of rotation thermal capacitance of molecule,
For diatomic and linear molecule,For isomolecule, Indicate the vibration thermal capacitance of molecule,
It can be calculated by formula (6),
Wherein, h is planck constant；kBFor Boltzmann constant, θintFor characteristic vibrational temperature；υ is vibration frequency；G is
The degeneracy of vibration mode, T0Indicate temperature.
Using formula (5) andThe real and imaginary parts of available single relaxation process:
Formula (7) are substituted into the A of formula (4)μIn expression formula, we are obtained
As can be seen that due toWith the change of ω, AμIt is almost unchanged.We enable Aμτ=1 ω in expression formula,
Approximation obtains the generic representation form of the single relaxation process of sound spectrum:
It is assumed that including W kind molecular species in mixed gas, there is N kind vibration mode (N >=W), multi-mode relaxation process has
Effect thermal capacitance be the single relaxation process of intramolecule the sum of:
WhereinIt is the external thermal capacitance of gas molecule l, alIt is composition ratio shared by gas molecule l；And τiIt is respectively
The inside effective heat capacity of i-th single relaxation process and relaxation time.Using formula (9) andIt can be with
Obtain formula (10):
Formula (10) are substituted into formula (4) and obtain the sound spectrum general purpose table of multi-mode relaxation process under conditions of ω τ=1
Show form:
According to formula (9), the thermal capacitance of multi-mode relaxation process can be expressed as the sum of the thermal capacitance of single relaxation process, such as public
Formula (12):
WhereinIndicate i-ththThe thermal capacitance of single relaxation process.
As formula (8), formula (13) are obtained:
Compare formula (13) and (11), the difference is that AiAnd AmAndWithDifference.
It is approximately consideredObtain formula (14):
Define peak valueAs relaxation time τiCorresponding relaxation strength, formula (14) can be write as public affairs
Formula (15):
In formula (15), εiAnd τiIt is defined as the single relaxation process in all inside in entire multi-mode relaxation process
Relaxation strength and the relaxation time.Therefore, as long as obtaining the acoustical absorptivity α of 2*N Frequency point by measurementr(ω) harmony
Fast c (ω), so that it may obtain 2*N μm(ω), to solve N number of ε from 2*N equation (15)iAnd τiValue, then by N
A εiAnd τiValue substitute into equation (15) in, so that it may obtain μmThe spectral line of (ω) about the π of ω=2 f rebuilds multi-mode relaxation mistake
Journey.
The velocity of sound and sound absorption system of two Frequency points are only measured in the algorithm and Zhang Kesheng article proposed relative to PL
Several methods, such as formula (16) and formula (17):
Formula (15) of the invention is included more mode reconstructions, can more accurately be weighed by 2*N Frequency point of measurement
Build relaxation spectral line.Two Frequency point measurement methods in algorithm and Zhang Kesheng article that PL is proposed are only N=1 in the present invention
Special case.
In a specific embodiment, it is preferable to use the measured value of four Frequency points, rebuilds whole molecule multi-mode relaxation
Process uses the data of 2*N=4 (N=2) a measurement point, rebuild the spectral line of N (N=2) a molecule multi-mode relaxation process.
In the present embodiment, preferably an acoustic sensor equipment job is in 40kHz, 125kHz, 215kHz and 1MHz frequency
Under, the mixed gas 40%CH of test4- 10%Cl2- 50%N2, as shown in Fig. 1 (a), the temperature of mixed gas is T=293K,
One atmospheric pressure.But in the present invention to gas componant, type etc. and without limitation.In test, measure under respective frequencies respectively
Acoustic velocity value c (ω) is 346.38ms-1、347.22m·s-1、347.49m·s-1、348.13m·s-1.Under corresponding frequencies
Acoustical absorptivity αr(ω) is 1.9546m respectively-1、5.3053m-1、 8.1506m-1、18.257m-1。
The sound spectrum value μ (ω) that four respective frequencies points are calculated using formula (2) is respectively 1.6926 × 10-2、
1.4737×10-2、1.3173×10-2With 6.3557 × 10-3, utilize formula (15) and four sound spectrum values, available reconstruct
2 relaxation strength ε afterwards1、ε2With relaxation time τ1、τ2Value is 1.527 × 10 respectively-2、7.916×10-3、3.523×10-6s
With 4.501 × 10-7S, and theoretic value is 1.542 × 10-2、8.169×10-3、3.511×10-6S and 4.497 × 10-7S,
As shown in Fig. 1 (a), it can be seen that result and theoretical value after reconstruction are coincide very much, it is difficult to be differentiated.It is more in solid line representation theory
Relaxation spectrum and the single relaxation spectral line after decomposition, dotted line indicate the single relaxation after the more relaxation spectrums implemented in the present invention and decomposition
The reconstruction result of spectral line.
Mixed gas 5%CH in another embodiment4- 95%N2, as shown in Fig. 1 (b), it is shown that in 92kHz and
The main relaxation spectral line (dotted line) of the PL algorithm reconstruct of 215kHz bis- Frequency points measurement and the present invention program 0.1kHz,
The whole relaxation spectral line (broken line) reconstructed after tetra- Frequency point measurements of 0.7kHz, 92kHz and 215kHz, the curve with theoretical value
(solid line) compares, it can be seen that the restructing algorithm of the present invention program is more effective, and theoretical curve fits like a glove.And PL algorithm mentions
Curve after the measurement method reconstruct of 2 Frequency points out is lost some relaxation information, such as Fig. 1 (b) left-hand component, PL algorithm
More like the reconstruct of a main relaxation process in the method for the present invention.
In another embodiment, mixed gas 10%CO2- 90%O2, temperature is respectively T=600K and T=450K,
Four Frequency points are selected to measure.As shown in Fig. 2 (a), mixed gas temperature is T=600K in the embodiment, every in figure
A lattice indicates the point of experimental data, it can be seen that the relaxation curve after reconstruction has on the right of Fig. 2 (a) with theoretical curve
A small amount of error, using least square and average weighted method, finally obtained curve and theoretical relaxation curve are (in Fig. 2 (b)
The curve of T=600K) it is consistent.In another embodiment, such as Fig. 2 (b), mixed gas 10%CO in the embodiment2- 90%O2,
Multi-mode molecular relaxation process when temperature is respectively T=450K and T=600K, 2 rebuild after more relaxation spectral lines and theoretically
Overlap of spectral lines together, thus accurately reconstruct mixed gas multi-mode relaxation process.
Several gases vibrate thermal capacitance in temperature 300K in the embodiment of the present inventionIt is specifically shown in down with simple T-beam υ
Table 1.
Several gases of table 1 vibrate thermal capacitance in temperature 300KWith simple T-beam υ
In the present invention program, in order to rebuild molecule multi-mode relaxation process, the preferred coverage test gas of the Frequency point of measurement
Main single relaxation process, four or more working frequency should be distributed in relaxation frequency range.In addition, side of the present invention
In case, four are also not necessarily limited to for data point, such as can be six, eight are waited 2*N, and specific data point can be according to reality
It tests condition and actual demand is selected.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include
Within protection scope of the present invention.
Claims (5)
1. a kind of method that mixed gas molecule multi-mode relaxation process is rebuild, which is characterized in that this method comprises the following steps:
(1) the sound spectrum expression formula of single relaxation is determined are as follows:
Wherein,Indicate the sum of translation and rotation thermal capacitance,Indicate the vibration thermal capacitance of molecule, the π of ω=2 f is angular frequency, and f is
Frequency, τ are the relaxation time,
(2) according to the sound spectrum expression formula of single relaxation, in ω τ=1, the generic representation shape of the single relaxation process of sound spectrum is obtained
Formula:
Wherein, μi(ω) indicates that dimensionless relaxation absorption coefficient, R are gas universal constant；
(3) assume in mixed gas to include W kind molecular species, have N kind vibration mode, the effective heat capacity of multi-mode relaxation process is
The sum of single relaxation process of intramolecule:
Wherein, τiIt is defined as the Henan time of the single relaxation process in inside in entire multi-mode relaxation process；
(4) peak value is definedFor relaxation time τiCorresponding relaxation strength, obtains:
Wherein,αr(ω) is acoustical absorptivity, and λ is wave length of sound, and c (ω) is acoustic velocity value；
(5) the acoustical absorptivity α of 2*N Frequency point is measuredr(ω) and velocity of sound c (ω), obtains 2*N μm(ω), from 2*N side
N number of ε is solved in journeyiAnd τiValue, and by N number of εiAnd τiValue substitute into step (4), obtain μmThe spectral line of (ω) about the π of ω=2 f,
Multi-mode relaxation process can be rebuild.
2. the method that a kind of mixed gas molecule multi-mode relaxation process according to claim 1 is rebuild, which is characterized in that
The vibration thermal capacitance of the moleculeAre as follows:
Wherein, g is the degeneracy of vibration mode, θintFor characteristic vibrational temperature, T0For temperature.
3. the method that a kind of mixed gas molecule multi-mode relaxation process according to claim 2 is rebuild, which is characterized in that
The characteristic vibrational temperature θintAre as follows:
Wherein: h is planck constant, kBFor Boltzmann constant, υ is vibration frequency.
4. the method that a kind of mixed gas molecule multi-mode relaxation process according to claim 1 is rebuild, which is characterized in that
The preparation method of the sound spectrum expression formula of the single relaxation are as follows:
(11) sound wave is propagated in gas, effective angular wave numberIt can be written as velocity of sound c (ω) and molecular relaxation absorption coefficientr
The form of (ω) expression:
(12) dimensionless relaxation absorption coefficient, the effective angular wave number of μ (ω) are indicated with μ (ω)Real and imaginary parts indicate:
Wherein,For effective angular wave numberImaginary part,For effective angular wave numberReal part；
(13)With effective heat capacityThere are following relationships:
Wherein, ρ0And p0The density and pressure of gas when respectively balancing；
(14) it enablesObtain the sound spectrum representation of gas multi-mode relaxation process:
μ (ω)=AμY (ω),
(15) sound spectrum of a multi-mode relaxation process is resolved into the sound spectrum expression formula of multiple single relaxation processes.
5. the method that a kind of mixed gas molecule multi-mode relaxation process according to claim 1,2 or 4 is rebuild, feature
It is, the negative of the real and imaginary parts of the multi-mode relaxation process are as follows:
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| CN108508054B (en) * | 2018-04-08 | 2020-06-30 | 许昌学院 | Hydrogen acoustic rotation relaxation detection method |
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| CN108645910B (en) * | 2018-06-04 | 2020-06-26 | 华中科技大学 | Method for detecting gas components based on inflection point of acoustic velocity spectral line |
| CN110161115B (en) * | 2019-05-23 | 2020-07-10 | 华中科技大学 | Gas component detection method and system based on sound velocity frequency dispersion intensity change rate |
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| CN112903811B (en) * | 2021-01-22 | 2023-12-01 | 湖北第二师范学院 | Acoustic sensing method for detecting concentration ratio of mixed gas |
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